I can't say I've thought about the mystery of the Third Murderer in Macbeth since my college days, and even then I didn't lose any sleep over it. Bullets for Macbeth, first published in 1976, proposes a new solution for which character the Third Murderer is, and ties it in to a murder.
Gene (whose last name I never did figure out) is a private investigator, although he actually works as an assistant to Hilary Quayle in her small PR firm. They're hired to advertise a production of Macbeth, whose director, an old friend of Hilary's, has a new idea for the Third Murderer and plans not to reveal it to anyone except the actor in question until the play opens. But Gene soon discovers that strange things are going on, events that the actors and director think are just due to Macbeth's bad luck--until someone is killed and the mysterious Third Murderer is a suspect. But no one knows who the Third Murderer is.
It's an interesting premise, but I don't know that it quite works. Kaye twists the plot into a pretzel in order to pull it off, keeping information from the reader to prolong the suspense. I was surprised at who the murderer is, but not in an "aha, of course!" way. I didn't really believe the person had done it, frankly. It didn't make a lot of sense, although I was more interested in the literary mystery of which character portrays the Third Murderer in the play.
I haven't read the first two books in this series so I don't know anything about the characters' history together, but I just couldn't warm up to Gene or Hilary. The book is also terribly dated, with lots of 70s slang, rampant sexism, and some coy but hostile references to gays. My attention wandered a lot. I stopped caring about who did it when I realized I couldn't figure it out because Kaye was withholding clues.
But it's a fast read and never actually made me mad. It just didn't grab me.